For \({\cal N}>4\) , the super-Cotton tensor [1]}, [2]}
is a completely antisymmetric tensor \({\cal W}^{IJKL}\) 
of dimension 1 constrained by [3]}
\(\nabla _{\alpha }^I {\cal W}^{JKLP} = \nabla _\alpha ^{[I} {\cal W}^{JKLP]}- \frac{4}{{\cal N}- 3} \nabla ^Q_{\alpha } {\cal W}^{Q [JKL} \delta ^{P] I} \ .\) 
